NC Math 3 Exponential and Log Functions

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain another number. For example, in log_b(a) = c, b is the base.

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation a^b = c to logarithmic form, write it as log_a(c) = b.

Front

What is the logarithmic identity for changing the base?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

Solve for x: 2^(x+6) = 2^5

Back

x = -1.

Front

Evaluate log_5(20) to the third decimal place.

Back

log_5(20) ≈ 1.861.

Front

Solve for b: 36^(3b) = 216^(b+4)

Back

b = 4.

Front

Solve for n: 2^(3n) = 4

Back

n = 2/3.

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4.